Finite Group Databasebeta

← #13279170

Subgroups — #13279170

Order 1792.

1738 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#387C211yesmaximal, characteristic, complemented
2C2×#89764C211yesmaximal, characteristic
3C2×#89761C211yesmaximal, characteristic
4C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
5C2×#89438C211yesmaximal, characteristic
6#11729320C211yesmaximal, characteristic, complemented
7#11729317C211yesmaximal, characteristic, complemented
8#11729291C211yesmaximal, characteristic
9#11727181C211yesmaximal, characteristic
10(C2×D7)⋊#95C211yesmaximal, characteristic
11#11727175C211yesmaximal, characteristic, complemented
12#11727162C211yesmaximal, characteristic
13#11727161C211yesmaximal, characteristic, complemented
14#11727160C211yesmaximal, characteristic, complemented
15#11727160C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×(C2×D7)⋊C4C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C7×#387—24no—
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38C2×C7⋊#95C2211yescharacteristic
39C2×C7⋊#95C2211yescharacteristic
40C2×C7⋊#95C2211yescharacteristic
41C2×C7⋊#95C2211yescharacteristic
42C2×C7⋊#95C2211yescharacteristic
43C2×C7⋊#95C2211yescharacteristic
44C2×C7⋊#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52#89764C418yescomplemented
53#89761—24no—
54C4×Dic7⋊C4—24no—
55#89438—24no—
56#14178—71nomaximal, Sylow
57C24×D7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C22×C4×D7—22no—
73C22×C4×D7—22no—
74C22×C4×D7—22no—
75C22×C4×D7—22no—
76C22×C4×D7—22no—
77C22×C4×D7—41no—
78C22×C4×D7—41no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—41no—
84C2×C7×C4⋊C4C2×C414yescomplemented
85C2×C42×C7—22no—
86C2×C42×C7—22no—
87C2×C42×C7—41no—
88C2×(C2×D7)⋊C4—22no—
89C2×(C2×D7)⋊C4—22no—
90C2×(C2×D7)⋊C4—22no—
91C2×(C2×D7)⋊C4—22no—
92C2×(C2×D7)⋊C4—22no—
93C2×(C2×D7)⋊C4—22no—
94C2×(C2×D7)⋊C4—22no—
95C2×(C2×D7)⋊C4—22no—
96C2×(C2×D7)⋊C4—22no—
97C2×(C2×D7)⋊C4—22no—
98C2×(C2×D7)⋊C4—41no—
99C2×(C2×D7)⋊C4—41no—
100C2×(C2×D7)⋊C4—41no—
101C2×(C2×D7)⋊C4—41no—
102C2×(C2×D7)⋊C4C2×C414yes—
103C2×(C2×D7)⋊C4C2×C414yes—
104C2×(C2×D7)⋊C4C2×C414yes—
105C2×(C2×D7)⋊C4Q814yes—
106C2×C4⋊Dic7—22no—
107C2×C4⋊Dic7—22no—
108C2×C4⋊Dic7—41no—
109C2×Dic7⋊C4—22no—
110C2×Dic7⋊C4—22no—
111C2×Dic7⋊C4—22no—
112C2×Dic7⋊C4—22no—
113C2×Dic7⋊C4—41no—
114C2×Dic7⋊C4—41no—
115C2×Dic7⋊C4C2×C414yescomplemented
116C2×Dic7⋊C4C2×C414yescomplemented
117C2×Dic7⋊C4D414yes—
118C2×C4×Dic7—22no—
119C2×C4×Dic7—22no—
120C2×C4×Dic7—22no—
121C2×C4×Dic7—22no—
122C2×C4×Dic7—22no—
123C2×C4×Dic7—22no—
124C2×C4×Dic7—22no—
125C2×C4×Dic7—41no—
126C2×C4×Dic7—41no—
127C7×#95—22no—
128C7×#95—22no—
129C7×#95—22no—
130C7×#95D414yes—
131C7⋊#95—22no—
132C7⋊#95—22no—
133C7⋊#95—22no—
134C7⋊#95—22no—
135C7⋊#95—22no—
136C7⋊#95—22no—
137C7⋊#95—22no—
138C7⋊#95—22no—
139C7⋊#95—41no—
140C7⋊#95—41no—
141C7⋊#95—41no—
142C7⋊#95—41no—
143C7⋊#95—41no—
144C7⋊#95C2×C414yescomplemented
145C2×#399—71no—
146C2×#387D711yescharacteristic, complemented
147C2×#385—71no—
148C2×C4×C4⋊C4—71no—
149C2×C4×C22⋊C4—71no—
150#1445—71no—
151#1441—71no—
152#1439—71no—
153#1437—71no—
154#1437—71no—
155#1436—71no—
156#1436—71no—
157#1436—71no—
158C4⋊#95—71no—
159C22⋊#95—71no—
160C24×C7C2411yescharacteristic
161C23×D7—21no—
162C23×D7—21no—
163C23×D7—21no—
164C23×D7—21no—
165C23×D7—21no—
166C23×D7—21no—
167C23×D7—21no—
168C23×D7—21no—
169C23×D7—21no—
170C23×D7—21no—
171C23×D7—21no—
172C23×D7—21no—
173C23×D7C22×C412yes—
174C23×D7C2×Q812yes—
175C23×D7#4112yes—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7C22×C412yes—
216C22×C4×C7C22×C412yes—
217C22×C4×C7C22×C412yes—
218C22×C4×C7C2×D412yes—
219C22×C4×C7C2×D412yes—
220C22×C4×C7C2×D412yes—
221C22×C4×C7C2×D412yes—
222C22×C4×C7C2×Q812yes—
223C22×C4×C7#4112yes—
224C22×C4×C7#4112yes—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—21no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7—21no—
242C22×Dic7—21no—
243C22×Dic7—21no—
244C22×Dic7—21no—
245C22×Dic7—21no—
246C22×Dic7—21no—
247C22×Dic7—21no—
248C22×Dic7—21no—
249C22×Dic7—21no—
250C22×Dic7—21no—
251C22×Dic7—21no—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7—21no—
255C22×Dic7—21no—
256C22×Dic7—21no—
257C22×Dic7—21no—
258C22×Dic7—21no—
259C22×Dic7—21no—
260C22×Dic7—21no—
261C22×Dic7—21no—
262C22×Dic7—21no—
263C22×Dic7—21no—
264C22×Dic7C22×C412yes—
265C22×Dic7C22×C412yes—
266C22×Dic7C22×C412yes—
267C22×Dic7C2×D412yes—
268C22×Dic7C2×D412yes—
269C22×Dic7C2×Q812yes—
270C22×Dic7#4112yes—
271C22×Dic7#4112yes—
272C22×Dic7#4112yes—
273C22×Dic7#4112yes—
274C2×C4×D7—28no—
275C2×C4×D7—44no—
276C2×C4×D7—44no—
277C2×C4×D7—44no—
278C2×C4×D7—44no—
279C2×C4×D7—44no—
280C2×C4×D7—44no—
281C7×C4⋊C4—28no—
282C7×C4⋊C4—44no—
283C42×C7—44no—
284(C2×D7)⋊C4—28no—
285(C2×D7)⋊C4—28no—
286(C2×D7)⋊C4—28no—
287(C2×D7)⋊C4—44no—
288(C2×D7)⋊C4—44no—
289(C2×D7)⋊C4—44no—
290C4⋊Dic7—44no—
291Dic7⋊C4—28no—
292Dic7⋊C4—28no—
293Dic7⋊C4—44no—
294C4×Dic7—28no—
295C4×Dic7—44no—
296C4×Dic7—44no—
297C24×C4—71no—
298C22×C4⋊C4—71no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4C2×D711yescharacteristic
303C22×C4⋊C4C2×D711yescharacteristic
304C22×C22⋊C4—71no—
305C22×C22⋊C4—71no—
306C22×C22⋊C4—71no—
307C22×C22⋊C4—71no—
308C22×C22⋊C4—71no—
309C22×C22⋊C4—71no—
310C22×C42—71no—
311C22×C42—71no—
312C22×C42—71no—
313C22×C42C2×D711yescharacteristic
314#399—78no—
315#387—24no—
316#385—144no—
317C4×C4⋊C4—144no—
318C4×C22⋊C4—144no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95—71no—
326C2×#95—71no—
327C2×#95—71no—
328C2×#95—71no—
329C2×#95—71no—
330C2×#95—71no—
331C2×#95—71no—
332C2×#95—71no—
333C2×#95C2×D711yescharacteristic
334C2×#95C2×D711yescharacteristic
335C2×#95C2×D711yescharacteristic
336C2×#95C2×D711yescharacteristic
337C23×C7C23×C411yescharacteristic
338C23×C7C22×D411yescharacteristic
339C23×C7C22×D411yescharacteristic
340C23×C7C22×Q811yescharacteristic
341C23×C7C2×#4111yescharacteristic
342C23×C7C2×#4111yescharacteristic
343C23×C7C2×#4111yescharacteristic
344C23×C7C2×#4111yescharacteristic
345C23×C7C2×#4111yescharacteristic
346C23×C7C2×#4111yescharacteristic
347C23×C7C2×#4111yescharacteristic
348C23×C7H(5,𝔽2)11yescharacteristic
349C23×C7H(5,𝔽2)11yescharacteristic
350C23×C7H(5,𝔽2)11yescharacteristic
351C23×C72−1+411yescharacteristic
352C22×D7—22no—
353C22×D7—22no—
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—22no—
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—22no—
365C22×D7—22no—
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—41no—
371C22×D7—41no—
372C22×D7—41no—
373C22×D7—41no—
374C22×D7—41no—
375C22×D7—41no—
376C22×D7—41no—
377C22×D7—41no—
378C22×D7—41no—
379C22×D7—41no—
380C22×D7—41no—
381C22×D7—41no—
382C22×D7—41no—
383C22×D7—41no—
384C22×D7—41no—
385C22×D7—41no—
386C22×D7C4×Q814yes—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—41no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—41no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7—41no—
424C2×C4×C7—41no—
425C2×C4×C7—41no—
426C2×C4×C7—41no—
427C2×C4×C7—41no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7C4×D414yes—
435C2×C4×C7C22⋊Q814yes—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—22no—
452C2×Dic7—22no—
453C2×Dic7—22no—
454C2×Dic7—22no—
455C2×Dic7—22no—
456C2×Dic7—22no—
457C2×Dic7—22no—
458C2×Dic7—22no—
459C2×Dic7—22no—
460C2×Dic7—41no—
461C2×Dic7—41no—
462C2×Dic7—41no—
463C2×Dic7—41no—
464C2×Dic7—41no—
465C2×Dic7—41no—
466C2×Dic7—41no—
467C2×Dic7—41no—
468C2×Dic7—41no—
469C2×Dic7—41no—
470C2×Dic7—41no—
471C2×Dic7—41no—
472C2×Dic7—41no—
473C2×Dic7—41no—
474C2×Dic7—41no—
475C2×Dic7—41no—
476C2×Dic7—41no—
477C2×Dic7—41no—
478C2×Dic7—41no—
479C2×Dic7—41no—
480C2×Dic7—41no—
481C2×Dic7—41no—
482C2×Dic7—41no—
483C2×Dic7C4×D414yes—
484C2×Dic7#12314yes—
485C4×D7—416no—
486C25—71no—
487C23×C4—71no—
488C23×C4—71no—
489C23×C4—71no—
490C23×C4—71no—
491C23×C4—71no—
492C23×C4—71no—
493C23×C4—71no—
494C23×C4—142no—
495C23×C4—142no—
496C23×C4—142no—
497C23×C4—142no—
498C23×C4—142no—
499C23×C4—281no—
500C23×C4—281no—
501C23×C4C22×D711yescharacteristic
502C23×C4C22×D711yescharacteristic
503C23×C4C22×D711yescharacteristic
504C23×C4C22×D711yescharacteristic
505C23×C4C22×D711yescharacteristic
506C23×C4C22×D711yescharacteristic
507C23×C4C22×D711yescharacteristic
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—41no—
513C2×C4⋊C4—74no—
514C2×C4⋊C4—74no—
515C2×C4⋊C4—74no—
516C2×C4⋊C4—142no—
517C2×C4⋊C4—142no—
518C2×C4⋊C4—142no—
519C2×C4⋊C4—142no—
520C2×C4⋊C4—142no—
521C2×C4⋊C4—142no—
522C2×C4⋊C4—281no—
523C2×C4⋊C4—281no—
524C2×C4⋊C4—281no—
525C2×C4⋊C4C4×D714yescomplemented
526C2×C22⋊C4—74no—
527C2×C22⋊C4—74no—
528C2×C22⋊C4—74no—
529C2×C22⋊C4—74no—
530C2×C22⋊C4—142no—
531C2×C22⋊C4—142no—
532C2×C22⋊C4—142no—
533C2×C22⋊C4—142no—
534C2×C22⋊C4—142no—
535C2×C22⋊C4—142no—
536C2×C22⋊C4—142no—
537C2×C22⋊C4—142no—
538C2×C22⋊C4—142no—
539C2×C22⋊C4—142no—
540C2×C22⋊C4—281no—
541C2×C22⋊C4—281no—
542C2×C22⋊C4—281no—
543C2×C22⋊C4—281no—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—41no—
547C2×C42—142no—
548C2×C42—142no—
549C2×C42—142no—
550C2×C42—142no—
551C2×C42—142no—
552C2×C42—142no—
553C2×C42—142no—
554C2×C42—281no—
555C2×C42—281no—
556#95—22no—
557#95—22no—
558#95—22no—
559#95—74no—
560#95—142no—
561#95—142no—
562#95—142no—
563#95—142no—
564#95—142no—
565#95—142no—
566#95—142no—
567#95—142no—
568#95—281no—
569#95—281no—
570#95—281no—
571#95—281no—
572#95—281no—
573#95C22⋊D714yes—
574C22×C7C2×C4×D411yescharacteristic
575C22×C7C2×C4×D411yescharacteristic
576C22×C7C2×C4×Q811yescharacteristic
577C22×C7C4×#4111yescharacteristic
578C22×C7C4×#4111yescharacteristic
579C22×C7#51811yescharacteristic
580C22×C7#52011yescharacteristic
581C22×C7C2×C22⋊Q811yescharacteristic
582C22×C7C2×#12311yescharacteristic
583C22×C7#52511yescharacteristic
584C22×C7#52511yescharacteristic
585C22×C7#52911yescharacteristic
586C22×C7#52911yescharacteristic
587C22×C7#52911yescharacteristic
588C22×C7#53311yescharacteristic
589C22×C7#53811yescharacteristic
590C22×C7#53911yescharacteristic
591C22×C7#54011yescharacteristic
592C22×C7#54211yescharacteristic
593C22×C7D4211yescharacteristic
594C22×C7#54611yescharacteristic
595C22×C7#54611yescharacteristic
596C22×C7#54711yescharacteristic
597C22×C7D4×Q811yescharacteristic
598C22×C7#55011yescharacteristic
599C22×C7#55011yescharacteristic
600C22×C7#55111yescharacteristic
601C22×C7#55111yescharacteristic
602C22×C7#55111yescharacteristic
603C22×C7#55211yescharacteristic
604C22×C7#55211yescharacteristic
605C22×C7#55411yescharacteristic
606C22×C7#55411yescharacteristic
607C22×C7#55411yescharacteristic
608C22×C7#55911yescharacteristic
609C2×D7—24no—
610C2×D7—24no—
611C2×D7—24no—
612C2×D7—42no—
613C2×D7—42no—
614C2×D7—42no—
615C2×D7—42no—
616C2×D7—42no—
617C2×D7—42no—
618C2×D7—42no—
619C2×D7—42no—
620C2×D7—42no—
621C2×D7—42no—
622C2×D7—42no—
623C2×D7—42no—
624C4×C7—24no—
625C4×C7—24no—
626C4×C7—42no—
627C4×C7—42no—
628C4×C7—42no—
629C4×C7—42no—
630C4×C7—81no—
631Dic7—24no—
632Dic7—24no—
633Dic7—42no—
634Dic7—42no—
635Dic7—42no—
636Dic7—42no—
637Dic7—81no—
638C24—72no—
639C24—72no—
640C24—72no—
641C24—141no—
642C24—141no—
643C24—141no—
644C24—141no—
645C24—141no—
646C24—141no—
647C24—141no—
648C24—141no—
649C24—141no—
650C24—141no—
651C24—141no—
652C24—141no—
653C24C23×D711yescharacteristic
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—72no—
694C22×C4—72no—
695C22×C4—72no—
696C22×C4—72no—
697C22×C4—72no—
698C22×C4—72no—
699C22×C4—72no—
700C22×C4—72no—
701C22×C4—72no—
702C22×C4—72no—
703C22×C4—148no—
704C22×C4—141no—
705C22×C4—141no—
706C22×C4—141no—
707C22×C4—141no—
708C22×C4—141no—
709C22×C4—141no—
710C22×C4—141no—
711C22×C4—141no—
712C22×C4—141no—
713C22×C4—141no—
714C22×C4—141no—
715C22×C4—141no—
716C22×C4—141no—
717C22×C4—141no—
718C22×C4—141no—
719C22×C4—141no—
720C22×C4—141no—
721C22×C4—141no—
722C22×C4—141no—
723C22×C4—141no—
724C22×C4—141no—
725C22×C4—141no—
726C22×C4—141no—
727C22×C4—141no—
728C22×C4—141no—
729C22×C4—141no—
730C22×C4—141no—
731C22×C4—141no—
732C22×C4—141no—
733C22×C4—141no—
734C22×C4—141no—
735C22×C4—141no—
736C22×C4—141no—
737C22×C4—141no—
738C22×C4—141no—
739C22×C4—141no—
740C22×C4—141no—
741C22×C4—141no—
742C22×C4—141no—
743C22×C4—284no—
744C22×C4—284no—
745C22×C4—284no—
746C22×C4—284no—
747C22×C4—284no—
748C22×C4—284no—
749C22×C4C2×C4×D712yes—
750C22×C4C2×C4×D712yes—
751C22×C4C2×C4×D712yes—
752C22×C4#115712yes—
753C22×C4D4×D712yes—
754C22×C4Q8×D712yes—
755C22×C4#116112yes—
756C22×C4C2×C22⋊D712yes—
757C22×C4C2×C22⋊D712yes—
758C22×C4C2×C22⋊D712yes—
759C4⋊C4—28no—
760C4⋊C4—44no—
761C4⋊C4—148no—
762C4⋊C4—148no—
763C4⋊C4—284no—
764C4⋊C4—284no—
765C22⋊C4—148no—
766C22⋊C4—148no—
767C22⋊C4—148no—
768C22⋊C4—284no—
769C22⋊C4—284no—
770C22⋊C4—284no—
771C42—44no—
772C42—148no—
773C42—284no—
774C42—284no—
775C2×C7C4×#12311yescharacteristic
776C2×C7C4×C22⋊Q811yescharacteristic
777C2×C7#233511yescharacteristic
778C2×C7#235911yescharacteristic
779C2×C7#236011yescharacteristic
780C2×C7#236611yescharacteristic
781C2×C7#236811yescharacteristic
782C2×C7#241811yescharacteristic
783C2×C7#242311yescharacteristic
784C2×C7#244911yescharacteristic
785C2×C7#245411yescharacteristic
786C2×C7#247111yescharacteristic
787C2×C7#247911yescharacteristic
788C2×C7#257511yescharacteristic
789C2×C7#258911yescharacteristic
790D7—44no—
791C23—74no—
792C23—142no—
793C23—142no—
794C23—142no—
795C23—142no—
796C23—142no—
797C23—142no—
798C23—142no—
799C23—142no—
800C23—142no—
801C23—142no—
802C23—142no—
803C23—142no—
804C23—142no—
805C23—142no—
806C23—142no—
807C23—142no—
808C23—142no—
809C23—142no—
810C23—281no—
811C23—281no—
812C23—281no—
813C23—281no—
814C23—281no—
815C23—281no—
816C23—281no—
817C23—281no—
818C23—281no—
819C23—281no—
820C23—281no—
821C23—281no—
822C23—281no—
823C23—281no—
824C23—281no—
825C23—281no—
826C23C22×C4×D711yescharacteristic
827C23C2×#115711yescharacteristic
828C23C2×D4×D711yescharacteristic
829C23#654811yescharacteristic
830C23C2×Q8×D711yescharacteristic
831C23C2×#116111yescharacteristic
832C23D7×#4111yescharacteristic
833C23D7×#4111yescharacteristic
834C23D7×#4111yescharacteristic
835C23D7×#4111yescharacteristic
836C23D7×#4111yescharacteristic
837C23#655311yescharacteristic
838C23#655311yescharacteristic
839C23#655411yescharacteristic
840C23C22×C22⋊D711yescharacteristic
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—74no—
889C2×C4—74no—
890C2×C4—142no—
891C2×C4—142no—
892C2×C4—142no—
893C2×C4—142no—
894C2×C4—142no—
895C2×C4—142no—
896C2×C4—142no—
897C2×C4—142no—
898C2×C4—142no—
899C2×C4—142no—
900C2×C4—142no—
901C2×C4—142no—
902C2×C4—142no—
903C2×C4—142no—
904C2×C4—142no—
905C2×C4—142no—
906C2×C4—142no—
907C2×C4—142no—
908C2×C4—142no—
909C2×C4—142no—
910C2×C4—142no—
911C2×C4—142no—
912C2×C4—142no—
913C2×C4—142no—
914C2×C4—2816no—
915C2×C4—281no—
916C2×C4—281no—
917C2×C4—281no—
918C2×C4—281no—
919C2×C4—281no—
920C2×C4—281no—
921C2×C4—281no—
922C2×C4—281no—
923C2×C4—281no—
924C2×C4—281no—
925C2×C4—281no—
926C2×C4—281no—
927C2×C4—281no—
928C2×C4—281no—
929C2×C4—281no—
930C2×C4—281no—
931C2×C4—281no—
932C2×C4—281no—
933C2×C4—281no—
934C2×C4—281no—
935C2×C4—281no—
936C2×C4—281no—
937C2×C4—281no—
938C2×C4C4×C22⋊D714yes—
939C2×C4#650914yes—
940C7#1417811yescharacteristic, complemented, Sylow
941C22—144no—
942C22—144no—
943C22—144no—
944C22—282no—
945C22—282no—
946C22—282no—
947C22—282no—
948C22—282no—
949C22—282no—
950C22—282no—
951C22—282no—
952C22—282no—
953C22—282no—
954C22—282no—
955C22—282no—
956C22#9021311yescharacteristic
957C22#9021411yescharacteristic
958C22#9021811yescharacteristic
959C22#9022211yescharacteristic
960C22C4×D4×D711yescharacteristic
961C22#9023611yescharacteristic
962C22#9024411yescharacteristic
963C22#9025011yescharacteristic
964C22C4×Q8×D711yescharacteristic
965C22C4×#116111yescharacteristic
966C22#9026911yescharacteristic
967C22#9027111yescharacteristic
968C22#9031811yescharacteristic
969C22#9032311yescharacteristic
970C22#9032711yescharacteristic
971C22#9033611yescharacteristic
972C22D7×#12311yescharacteristic
973C22#9034511yescharacteristic
974C22#9034811yescharacteristic
975C22#9035011yescharacteristic
976C22#9038111yescharacteristic
977C22#9038111yescharacteristic
978C22#9038211yescharacteristic
979C22#9038911yescharacteristic
980C22#9039611yescharacteristic
981C22#9039711yescharacteristic
982C22#9039911yescharacteristic
983C22#9040111yescharacteristic
984C22C2×C4×C22⋊D711yescharacteristic
985C22D4×C22⋊D711yescharacteristic
986C22C2×#650911yescharacteristic
987C22#9051511yescharacteristic
988C22#9051911yescharacteristic
989C22#9052011yescharacteristic
990C22#9052511yescharacteristic
991C4—24no—
992C4—24no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—81no—
998C4—144no—
999C4—144no—
1000C4—282no—
1001C4—282no—
1002C4—282no—
1003C4—282no—
1004C4—561no—
1005C2—284no—
1006C2#1173238511yescharacteristic
1007C2#1173240111yescharacteristic
1008C2#1173241011yescharacteristic
1009C2#1173242711yescharacteristic
1010C2#1173245211yescharacteristic
1011C2#1173253011yescharacteristic
1012C2#1173255311yescharacteristic
1013C2#1173275511yescharacteristic
1014C2#1173968711yescharacteristic
1015C2#1173978811yescharacteristic
1016C2C4×#650911yescharacteristic
1017C2#1174020911yescharacteristic
1018C2#1174034111yescharacteristic
1019C2#1174047511yescharacteristic
1020C2#1174052511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#387C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#387D7
hypocenterC7#14178
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#387

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C7×#387C2semidirect
4. C2×C4×Dic7⋊C4C2semidirect
6. #11729320C2semidirect
7. #11729317C2semidirect
11. #11727175C2semidirect
13. #11727161C2semidirect
14. #11727160C2semidirect
15. #11727160C2semidirect
52. #89764C4semidirect
84. C2×C7×C4⋊C4C2×C4semidirect
115. C2×Dic7⋊C4C2×C4semidirect
116. C2×Dic7⋊C4C2×C4semidirect
144. C7⋊#95C2×C4semidirect
146. C2×#387D7semidirect
525. C2×C4⋊C4C4×D7semidirect
940. C7#14178semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C7×#3872
C2×#897642
C2×#897612
C2×C4×Dic7⋊C42
C2×#894382
#117293202
#117293172
#117292912
#117271812
(C2×D7)⋊#952
#117271752
#117271622
#117271612
#117271602
#141787